(ii) A remarkable class of \(C\) -concave mappings is the subclass
of \(\mathcal {P}(\mathbb {X},\mathbb {Y})\)  formed by the superlinear operators taking values
in a Kantorovich space \(\mathbb {Y}\)  (i.e. a Dedekind complete normed vector
lattice), partially ordered by a cone \(C\) .
Following [1]}, a mapping \(h\in \mathcal {P}(\mathbb {X},\mathbb {Y})\)  is said to
be superlinear if \(h(x)+h(z)\le _{{}_C}h(x+z)\) , for every \(x,\, z\in \mathbb {X}\) .
It is well known that, as a consequence of the
Hahn-Banach-Kantorovich theorem (see [2]}), any superlinear
operator admits the following infimal representation
\(h(x)=\min {}_{\le _{{}_C}}\lbrace \Lambda x:\ \Lambda \in \overline{\partial }h\rbrace ,\) 
